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arXiv · 2006.01564

Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions

Katsukuni Nakagawa
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Abstract

Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is compact. Using this Banach space, we establish the trace formula and spectral representation of Ruelle zeta functions for a certain class of super-continuous functions. Our results include, as a special case, the classical trace formula and spectral representation for the class of locally constant functions.

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Katsukuni Nakagawa. 2020-06-02. Compactness of Transfer Operators and Spectral Representation of Ruelle Zeta Functions for Super-continuous Functions. https://doi.org/10.3934/dcds.2020282

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